"We made a good start last month, and this week we'll be getting into the real substance", Davis said in a statement released by his office. How much substantial progress could be made during the talks remains to be seen.
Earlier on Sunday, Chancellor Philip Hammond had said senior British government ministers were becoming convinced of the need for transitional arrangements to reduce disruption as Britain leaves the EU.
And Foreign Secretary Boris Johnson then fanned the flames when he said Brussels could "go whistle" if it expected the United Kingdom to pay a hefty "divorce bill" in respect of its outstanding financial obligations.
Davis is attempting to accelerate a dialogue between himself and Barnier, open divisions in British Prime Minister Theresa May's cabinet make it hard to determine the British course of action, Bloomberg News said Monday.
An unnamed senior Cabinet minister is quoted in The Daily Telegraph saying: "What's really going on is that the Establishment, the Treasury, is trying to f*** it up".
Porter renewed a call - made in March - that leaving the European Union should not simply be a transfer of powers from Brussels to Westminster, Holyrood, Stormont and Cardiff Bay but should also offer "new legislative freedoms and flexibilities", which will benefit councils and businesses.
A University of Sussex study focusing on the food supply showed the potential consequences of no deal: tariffs of as much as 22 percent, the need to replace a "vast array" of food standard institutions across Europe, and tricky questions of how to replace European Union subsidies and farm laborers who often take seasonal work that British citizens don't want. He declined to identify the sources who had indicated which leaders he was referring to. If that happens, parallel negotiations can commence on Britain's future relationship with the European Union after Brexit. British industry of medicine and aviation have recently voiced their concerns. "This government is facing a ticking clock over the Brexit negotiations", Hammond said on Sunday.
It is the second round of formal talks.
The talks are the first full round of negotiations that formally began last month with a one-day session to agree on a timetable. Beyond these headline goals, they will discuss how to ensure a smooth transition on Brexit Day, a set of topics known as "other separation issues" where the ECJ looms large.
The negotiation is expected to be complicated, as May's minority government will face challenges at every step in the process.
Davis added that apart from citizens' rights and the UK's exit bill, Northern Ireland issues are also a priority of these talks.